Yes, it is possible to create an alert and send to the desired email/sms etc. when a user logins the azure virtual machine.
Here is how I am setting it up to get an email alert.
VM Blade >Monitoring> Diagnostic settings>Enable Guest Level Monitoring Make sure that you have a storage account at the same region
'Enable' Insights under Monitoring>Insights
Monitoring>Alerts->Create New Alert Rule
Select a Custom query as follows
VMConnection | where Direction == "inbound" | where Protocol == "tcp" | where DestinationPort == 3389
Create an Action Group to send alerts
Select the preferred way of getting alerts
Select the preferred Alert Logic
Set Alert details as per the preference
Now you are ready to save the alert rules. It may take couple of minutes to start getting the alerts. Then you will start receiving the alerts something like follows when there is an RDP connection detected like following message in your inbox
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